منابع مشابه
On self-dual doubly-even extremal codes
Let C be a binary linear self-dual doubly-even code of length n and minimal weight d. Such codes exist only if 12 = 0 (mod 8). We put II = 24r + 8s, s = 0, 1, 2. It follows from the work of Gleason [2] and of Mallows and Sloane [6] that d s 4r + 4. C is called extremal if d = 4r + 4. In the following, an extremal code means a binary linear self-dual doubly-even extremal code. We use the set-the...
متن کاملAutomorphisms of doubly-even self-dual binary codes
The automorphism group of a binary doubly-even self-dual code is always contained in the alternating group. On the other hand, given a permutation group G of degree n there exists a doubly-even self-dual G-invariant code if and only if n is a multiple of 8, every simple self-dual F2G-module occurs with even multiplicity in F n 2 , and G is contained in the alternating group.
متن کاملLinear programming bounds for doubly-even self-dual codes
We give a new proof of the Mallows-Sloane bound on the minimum distance of doubly-even self-dual codes. The proof avoids using the Gleason theorem and invariant theory. It is based on a special choice of the polynomial in the conventional linear programming approach.
متن کاملType II Codes, Even Unimodular Lattices, and Invariant Rings
In this paper, we study self-dual codes over the ring Z 2k of the integers modulo 2k with relationships to even unimodular lattices, modular forms, and invariant rings of 1 nite groups. We introduce Type II codes over Z 2k which are closely related to even unimodular lattices, as a remarkable class of self-dual codes and a generalization of binary Type II codes. A construction of even unimodula...
متن کاملComplete weight enumerators of generalized doubly-even self-dual codes
For any q which is a power of 2 we describe a finite subgroup of GLqðCÞ under which the complete weight enumerators of generalized doubly-even self-dual codes over Fq are invariant. An explicit description of the invariant ring and some applications to extremality of such codes are obtained in the case q 1⁄4 4: r 2003 Elsevier Inc. All rights reserved.
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ژورنال
عنوان ژورنال: Journal of the Mathematical Society of Japan
سال: 1991
ISSN: 0025-5645
DOI: 10.2969/jmsj/04310067